IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-03887413.html
   My bibliography  Save this paper

Measuring adequately the benefit of diversification in the extreme quantiles: An inquiry into covariation on the brink of catastrophe

Author

Listed:
  • Pierre-Charles Pradier

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 UFR02 - Université Paris 1 Panthéon-Sorbonne - École d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Guillaume Rideau

    (BPCE - BPCE)

  • Sakina Rrguiti

    (UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, BPCE - BPCE)

Abstract

The aim of this work is to better understand the nature of covariation in the vicinity of extremes on financial data and assess whether the usual assumptions and covariation measures fits the actual data. For simplicity, we consider pairs of random variables. In order to identify the shape of the covariation all along the distribution, and particularly as the extreme quantiles are approached, we describe the contribution of each of the variables from a random couple to the quantiles of the weighted sum of these variables. This approach makes sense since it can be interpreted in terms of Value-at-Risk in a financial institution: the VaR of the sum of variables may represent the capital requiremet for a diversified conglomerate, while the sum of VaR of the variables would correspond to the capital requirements for the components of the conglomerate, without taking diversification into account. The ratio of these two quantities appears as a good measure of both the benefit of diversification and the decorrelation of variables. We thus compare the values of quantiles and ratio taken from a representative dataset to the values obtained from various simulations relying on the usual assumptions. The result of this comparison is that the usual assumptions do not correctly model the covariation of the real-word data. In particular, the usual assumptions tend to exaggerate the correlation in the vicinity of extreme loss while the benefit of diversification is uniform across distribution. Additional simulations and modelling assumptions may be required to assess the generality of this result.

Suggested Citation

  • Pierre-Charles Pradier & Guillaume Rideau & Sakina Rrguiti, 2022. "Measuring adequately the benefit of diversification in the extreme quantiles: An inquiry into covariation on the brink of catastrophe," Post-Print halshs-03887413, HAL.
  • Handle: RePEc:hal:journl:halshs-03887413
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03887413
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-03887413/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Smith, Keith V & Schreiner, John C, 1969. "A Portfolio Analysis of Conglomerate Diversification," Journal of Finance, American Finance Association, vol. 24(3), pages 413-427, June.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    2. David Neděla & Sergio Ortobelli & Tomáš Tichý, 2024. "Mean–variance vs trend–risk portfolio selection," Review of Managerial Science, Springer, vol. 18(7), pages 2047-2078, July.
    3. José Santiago Fajardo Barbachan & Aquiles Rocha de Farias & José Renato Haas Ornelas, 2008. "A Goodness-of-Fit Test with Focus on Conditional Value at Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 6(2), pages 139-155.
    4. Vincenzo Candila, 2013. "A Comparison of the Forecasting Performances of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    5. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    6. Eisenberg, Larry, 2011. "Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite," Journal of Financial Stability, Elsevier, vol. 7(1), pages 10-18, January.
    7. Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
    8. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    9. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    11. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    12. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
    13. Rachev, Svetlozar & Jasic, Teo & Stoyanov, Stoyan & Fabozzi, Frank J., 2007. "Momentum strategies based on reward-risk stock selection criteria," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2325-2346, August.
    14. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    15. Daniel Velásquez-Gaviria & Andrés Mora-Valencia & Javier Perote, 2020. "A Comparison of the Risk Quantification in Traditional and Renewable Energy Markets," Energies, MDPI, vol. 13(11), pages 1-42, June.
    16. Budhi Surya & Ryan Kurniawan, 2014. "Optimal Portfolio Selection Based on Expected Shortfall Under Generalized Hyperbolic Distribution," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 193-236, September.
    17. Kouaissah, Noureddine, 2021. "Using multivariate stochastic dominance to enhance portfolio selection and warn of financial crises," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 480-493.
    18. Adabi Firouzjaee , Bagher & Mehrara , Mohsen & Mohammadi , Shapour, 2014. "Optimal Portfolio Selection for Tehran Stock Exchange Using Conditional, Partitioned and Worst-case Value at Risk Measures," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 9(1), pages 1-30, October.
    19. George Kouretas & Leonidas Zarangas, 2005. "Conditional autoregressive valu at risk by regression quantile: Estimatingmarket risk for major stock markets," Working Papers 0521, University of Crete, Department of Economics.
    20. Tokat, Yesim & Rachev, Svetlozar T. & Schwartz, Eduardo, 2000. "The Stable non-Gaussian Asset Allocation: A Comparison with the Classical Gaussian Approach," University of California at Santa Barbara, Economics Working Paper Series qt9ph6b5gp, Department of Economics, UC Santa Barbara.

    More about this item

    Keywords

    Financial conglomerates; Diversification; Value-at-Risk; Capital requirement;
    All these keywords.

    JEL classification:

    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-03887413. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.